When asked to calculate the number of multiples in an interval, we usually take the difference between the first and last multiples in that interval, divide it by the multiple in question, and then add one. I have found that if we just take the edges of the interval instead of the first and last multiple, and then complete the same operation, we get the same result by always rounding down.
The example I attached is from (I’m Overwhelmed) Arithmetic Progress Quiz #3 Q14
It took me a lot of time to figure out the first and last multiples. However, just doing the operation with 407 to 1952 gave me 220.71, which I just rounded down to 220. I think this technique is quicker and makes sense mathematically.
Try from 401 to 1959 instead.
Right, it seems like this method sometimes leads to close but incorrect answers. Thanks!